Optimal resource control of a food chain with weak Allee effect and antipredator behaviour

Abstract The aim of this paper is to study a nonautomonous food chain model with three trophic levels: producers (plants), primary consumers (herbivores) and secondary consumers (carnivores). The model includes some realistic biological assumptions such as carrying capacity, seasonal reproduction, rigid social structure and the inclusion of antipredatory behaviour. Results concerning existence, uniqueness, positivity, uniform boundedness of the solution and local stability analysis of the (uncontrolled) model are presented. An optimal control problem related to primary consumer’s biomass is formulated. Existence and uniqueness of the optimal control is proved. Numerical simulation of both uncontrolled and controlled cases is presented. A study on the control efficiency is also presented.